Towards a Methodology for Ontology Based Model Engineering

Towards a methodology for ontology based model engineering

Nicola Guarino and Christopher Welty†

LADSEB/CNR Padova, Italy {guarino,welty}@ladseb.pd.cnr.it http://www.ladseb.pd.cnr.it/infor/ontology/ontology.html Phone: +39 049 829 57 51 Fax: +39 049 829 57 63 † on sabbatical from Vassar College, Poughkeepsie, NY

Abstract The Formal Tools of Ontological Analysis The philosophical discipline of Ontology is evolving towards an engineering discipline, and in this evolution the Our methodology is based on four fundamental ontologi- need for a principled methodology has clearly arisen. In cal notions, which will be discussed in this section: identity, this paper, we brieﬂy discuss our recent work towards devel- unity, rigidity, and dependence. We shall represent the oping a methodology for ontology-based model engineering. behavior of a property with respect to these notions by This methodology builds on previous methodology efforts, means of a set of meta-properties. Our goal is to show how and is founded on important analytic notions that have been these meta-properties impose some constraints on the way drawn from Philosophy and adapted to Engineering: identity, subsumption is used to model a domain. unity, rigidity, and dependence. We demonstrate how these techniques can be used to analyze properties, which clariﬁes many misconceptions about taxonomies and helps bring substantial order to ontologies. Preliminaries

Let’s assume we have a first-order language L0 (the model- Introduction ing language) whose intended domain is the world to be modeled, and another first order language (the meta-lan- Ontologies are becoming increasingly popular in prac- L1 tice, and the number of poor quality ontologies have made guage) whose constant symbols are the predicates of L0. clear the need for a principled methodology for building Our meta-properties will be represented by predicate sym- them. Perhaps the most common problem we have seen in bols of L1. Primitive meta-properties will correspond to practice with ontologies is that, while they are expected to axiom schemes of L0. When a certain axiom scheme holds bring order and structure to information, their taxonomic in L0 for a certain property, then the corresponding meta- structure is often poor and confusing. This is typically property holds in L1. This correspondence can be seen as a exemplified by the unrestrained use of subsumption to system of reflection rules between L and L , which allow accomplish a variety of reasoning and representation tasks. 0 1 us to define a particular meta-property in our meta-lan- For example, in previous work (Guarino, 1999) several unclear uses of the is-a relation in existing ontologies were guage, avoiding a second-order logical definition. Meta- identified, such as: properties will be used as analysis tools to characterize the ontological nature of properties in L0, and will always be 1. a physical object is an amount of matter (Pangloss) defined with respect to a given conceptualization. 2. an amount of matter is a physical object (WordNet) We shall denote primitive meta-properties by bolded let- This striking dissimilarity poses a difficult integration prob- ters preceded by the sign “+”, “-” or “~” corresponding to lem, since the standard approach of generalizing overlap- carrying the meta-property, not carrying the meta-property, ping concepts would not work, and shows that even the and anti the meta-property. The latter will be used to denote most experienced modelers need some guidance for using special restrictions that are stronger than the simple nega- subsumption consistently. tion, and will be described in more detail, when relevant, In this paper we show how a rigorous analysis of the for each meta-property. We use the notation φM to indicate ontological meta-properties of taxonomic nodes can help φ using the subsumption relation in a disciplined way. These that the property has the meta-property M. meta-properties are based on the philosophical notions of We shall furthermore adopt a first order logic with iden- rigidity, identity, unity, and dependence. They impose some tity. This will be occasionally extended to a simple tempo- constraints on the subsumption relation that clarify many ral logic, where all predicates are temporally indexed by misconceptions about taxonomies – misconceptions that means of an extra argument. If the time argument is omitted normally turn taxonomies into a tangled mess. We discuss for a certain predicate φ, then the predicate is assumed to be these misconceptions by means of real examples, and show time invariant, that is ∃tφ()xt, →∀t φ()xt, . Note that the how our analysis can bring true order to taxonomies, facili- identity relation will be assumed as time invariant: if two tating their understanding, comparison and integration. things are identical, they are identical forever. This means This is a first step towards a general methodology for ontol- that Leibniz’s rule holds with no exceptions. ogy-driven conceptual analysis (ODCA) which combines the established tradition of formal ontology in Philosophy We also adopt a time-indexed mereological relation with the needs of information systems design. P(x,y,t), meaning that x is a (proper or improper) part of y at time t, satisfying the minimal set of axioms and definitions change, and which must not? And how can we reidentify an (adapted from (Simons, 1987), p. 362) shown in Table 1. instance of a certain property after some time? The former issue leads to the notion of rigidity, discussed below, while ∧ ¬ = (proper part) PP(x,y,t) =def f(x,y,t) x y the latter is related to the distinction between synchronic ∃ ∧ O(x,y,t) =def z(P(z,x,t) P(z,y,t)) (overlap) and diachronic identity. An extensive analysis of these P(x,y,t) → E(x,t) ∧ E(y,t) (actual existence of parts) issues in the context of conceptual modeling has been made P(x,y,t) ∧ P(y,x,t) → x=y (antisymmetry) elsewhere (Guarino & Welty, 2000b). P(x,y,t) ∧ P(y,z,t) → P(x,z,t) (transitivity) Finally, it is important to note that, while we use exam- PP(x,y,t) → ∃z(PP(z,y,t) ∧ ¬O(z,x,t)) (weak supplementation) ples to clarify the notions central to our analysis, the examples are not the point of this paper. The everyday use of Table 1. Axiomatization of the part relation. these analysis tools ultimately depend on the assumptions Our domain of quantification will be that of possibilia. resulting from our conceptualization of the world (Guarino, That is, the extension of predicates will not be limited to 1998). For example, the decision as to whether a cat what exists in the actual world, but to what exists in any remains the same cat after it loses its tail, or whether a possible world (Lewis, 1983). For example, a predicate like statue is identical with the marble it is made of, are ulti- “Unicorn” will not be empty in our world, although no mately the result of our sensory system, our culture, etc. instance has actual existence there. Actual existence is The aim of the present analysis is to clarify the formal tools therefore different from existential quantification (“logical that can both make such assumptions explicit, and reveal existence”), and will be represented by the temporally the logical consequences of them. When we say, e.g. that indexed predicate E(x,t), meaning that x has actual exist- “having the same fingerprint” may be considered an iden- ence at time t (Hirst, 1991). tity criterion for PERSON, we do not mean to claim this is the universal identity criterion for PERSONs, but that if this Finally, in order to avoid trivial cases in our meta-prop- were to be taken as an identity criterion in some conceptu- erty definitions, we shall implicitly assume the property alization, what would that mean for the property, for its variables as restricted to discriminating properties instances, and its relationships to other properties? (Guarino, Carrara & Giaretta, 1994), i.e. properties P such that ¸∃xP() x ∧¸∃xP¬()x. Rigidity The Basic Notions A rigid property has been defined in (Guarino, Carrara & The notion of identity is at the core of our methodology. Giaretta, 1994) as a property that necessarily holds for all Despite its fundamental importance in Philosophy, it has its instances. For example, we normally think of PERSON been slow in making its way into the practice of conceptual as rigid; if x is an instance of PERSON, it must be an modeling, although it has been recognized from time to instance of PERSON in every possible world. The STU- time by various communities. In object-oriented languages, DENT property, on the other hand, is normally not rigid; we for example, uniquely identifying an object (as a collection can easily imagine an entity moving in and out of the STU- of data) is critical, in particular when a system has persis- DENT property while being the same individual. This tence or distributed components (Wieringa, De Jonge & notion was later refined in (Guarino, 1998), as shown in Spruit, 1994). In databases, globally unique id’s have been Table 2, where the notion of anti-rigidity was added to gain introduced into most commercial systems to address this φ is a necessary property for all its Rigid φ+R issue. These solutions approach the notion of identity we instances use here, but do not account for it completely, as they Non- φ is not a necessary property of all its merely provide a framework for identifying unique descrip- φ-R Rigid instances tions and not for understanding the nature of the identity φ relationship that holds among the entities they describe. Anti- φ~R is an optional property for all its Understanding the distinctions and similarities between Rigid instances identity and unity appears to be of crucial importance. Table 2. Rigidity behavior for a property φ. These notions are different, albeit closely related and often confused under a generic notion of identity. Strictly speak- a further restriction. The ~R meta-property is subsumed by ing, identity is related to the problem of distinguishing a –R, but is stronger, as the former constrains all instances of specific instance of a certain class from other instances by a property and the latter, as the simple negation of +R, con- means of a characteristic property, which is unique for it strains at least one instance. Anti-rigidity attempts to cap- (that whole instance). Unity, on the other hand, is related to ture the intuition that all instances of certain properties the problem of distinguishing the parts of an instance from must possibly not be instances of that property. Consider the rest of the world by means of a unifying relation that the property STUDENT, for example: in its normal usage, binds them together (not involving anything else). For every instance of student is not necessarily so. example, asking “Is that my dog?” would be a problem of Rigidity as a meta-property is not “inherited” by sub- identity, whereas asking “is the collar part of my dog?” properties of properties that carry it, e.g. if we have PER- would be a problem of unity. SON+R and ∀x STUDENT() x →PERSON() x then we know Both notions encounter problems when time is involved. that all instances of STUDENT are necessarily instances of The classical one is that of identity through change: in PERSON, but not necessarily (in the modal sense) order to account for common sense, we need to admit that instances of STUDENT, and we furthermore have STU- an individual may remain the same while exhibiting differ- DENT~R. In simpler terms, an instance of STUDENT can ent properties at different times. But which properties can cease to be a student but may not cease to be a person. Identity evant and not tautological, and (6) ensures that Γ is not trivially false. In the philosophical literature, an identity condition (IC) for φ ICs are “inherited” along a hierarchy of properties, in the a arbitrary property is usually defined as a suitable rela- φ()→ ϕ() Γ tion ρ satisfying the following formula: sense that, if x x and, for example, is a necessary IC for ϕ, then (3) above will hold for φ replacing ϕ. φ()x ∧ρ φ()y→(()xy, ↔x=y) (1) Definition 4 A non-rigid property carries an IC Γ iff it is Since identity is an equivalence relation, it follows that ρ subsumed by a rigid property carrying Γ. φ restricted to must also be an equivalence relation. For Definition 5 Any property carrying an IC is marked with example, the property PERSON can be seen as carrying an the meta-property +I (-I otherwise). IC if relations like having-the-same-SSN or having-the- same-fingerprints are assumed to satisfy (1). Definition 6 A property φ supplies an IC Γ iff i) it is rigid; As discussed in more detail elsewhere (Guarino & Welty, ii) it carries Γ; and iii) Γ is not carried by all the properties 2000b), the above formulation has some problems, in our subsuming φ. This means that, if φ inherits different (but opinion. The first problem is related to the need of distin- compatible) ICs from multiple properties, it still counts as guishing between supplying an IC and simply carrying an supplying an IC. IC: it seems that non-rigid properties like STUDENT can only carry their ICs, inheriting those supplied by their sub- Definition 7 Any property supplying an IC is marked with suming rigid properties like PERSON. The intuition behind the meta-property +O (-O otherwise). The letter “O” is a this is that, since the same person can be a student at differ- mnemonic for “own identity”. ent times in different schools, an IC allegedly supplied by STUDENT (say, having the same registration number) may From the above definitions, it is obvious that +O implies be only local, within a certain studenthood experience. It +I and +R. For example, both PERSON and STUDENT do would not supply therefore a “global” condition for iden- carry identity (they are therefore +I), but only the former tity, satisfying (1) only as a sufficient condition, not as a supplies it (+O). Supplying an IC is analogous to defining necessary one. the equality predicate for a class in an object-oriented language, except that ICs can not be “overridden” by a sub- The second problem regards the nature of the ρ relation: property, merely augmented. See the “Identity constraints” what makes it an IC, and how can we index it with respect section below for further discussion of this. to time to account for the difference between synchronic and diachronic identity? Definition 8 Any property carrying an IC (+I) is called a Finally, deciding whether a property carries an IC may sortal (Strawson, 1959). be difficult, since finding a ρ that is both necessary and suf- Notice that to recognize that a property is a sortal we are ficient for identity is often hard, especially for natural kinds not forced to know which IC it carries: as we shall see, dis- and artifacts. tinguishing between sortals and non-sortals is often enough For these reasons, we introduce below a notion of iden- to start bringing order to taxonomies. tity conditions that have the following characteristics: i) they can only be supplied by rigid properties; ii) they re- formulate the ρ relation above in terms of a formula that Unity explicitly takes two different times into account, allowing Before addressing what it means for a certain property to the distinction between synchronic (same time) and diach- carry a unity condition (UC), we must first clarify what it ronic (different times) identity; iii) they can be only suffi- means for a certain object to have a UC, that is to be a cient or only necessary. whole. Definition 1 Let φ be a rigid property, and Γ(x,y,t,t') a for- Definition 9 Let ω be an equivalence relation. At a given mula containing x,y,t,t' as the only free variables, such that time t, an object x is a contingent whole under ω if: ¬∀xytt’(Γ(x,y,t,t') ↔ x=y) (2) ∀y(P(y,x,t) → ∀z(P(z,x,t) ↔ ω(z, y,t))) (7)

We say that φ carries the IC Γ iff one of the following con- We can read the above formula as follows: at time t, ditions is verified: each part of x must be bound by ω to all other parts and nothing else. In other words, (7) expresses a condition of Definition 2 Γ is a necessary IC carried by φ when: maximal self-connectedness according to a suitable relation of “generalized connection,” ω. Depending on the ontologi- E(x,t) ∧ φ(x,t) ∧ E(y,t') ∧ φ(y,t’) ∧ x=y → Γ(x,y,t,t') (3) cal nature of such a generalized connection relation, we ¬∀xy(E(x,t) ∧ φ(x,t) ∧ E(y,t) ∧ φ(y,t’) → Γ(x,y,t,t')) (4) may distinguish three main kinds of unity for concrete entities (i.e., those having a spatio-temporal location): Γ φ • Topological unity: based on some kind of topological Definition 3 is a sufficient IC carried by when: connection (a piece of coal, a lump of coal) E(x,t) ∧ φ(x,t) ∧ E(y,t') ∧ φ(y,t’) ∧ Γ(x,y,t,t') → x=y (5) • Morphological unity: based on shape (a ball, a constella- tion) ∃xytt' Γ(x,y,t,t'). (6) • Functional unity (a hammer, a bikini) As the examples show, nothing prevents a whole from In the formulas above, (2) guarantees that Γ is bound to having parts that are themselves wholes (with a different identity under a certain sortal, and not to arbitrary identity, UC). This can be the foundation of a theory of pluralities, (4) is needed to guarantee that the last conjunct in (3) is rel- which is however out of this paper’s scope. We define a stronger notion of whole by assuming that a For example, a castle and the lump of bricks it is consti- UC must hold for an object throughout its existence, i.e. by tuted of are formed of the same constituent parts, and the assuming unity as an essential property: castle cannot exist without the lump of bricks also existing (but not vice-versa). A property which is externally depen- Definition 10 Let ω be an equivalence relation. An object x ω dent on some other property will be marked with the meta- is an intrinsic whole under if, at any time where x exists, property +D. it is a contingent whole under ω. An important remark is that, if an object is always atomic Constraints and Assumptions (i.e., it has no proper parts), then it is an intrinsic whole under the identity relation. We are now in the position to Let us now discuss the constraints that follow from our state the following: definitions. We distinguish between four kinds of constraints, which are largely overlooked in many practical φ Definition 11 A property carries a unity condition (+U) cases (Guarino, 1999), (Guarino & Welty, 2000). Concrete iff there exists an equivalence relation ω such that all its examples will be discussed at the end of this paper. In the instances are intrinsic wholes under ω. following, we take φ and ψ to be arbitrary properties. Notice that the above definition does not imply a second order existential quantification in order to get the relation Rigidity constraints ω: simply, if such relation is part of our ontology, then φ+U. φ~R can't subsume ψ+R (8) It is important to make clear that carrying a UC does not imply carrying a necessary IC. This is due to the way Defi- This constraint follows immediately from the definitions nition 2 is formulated. To see that, suppose that φ carries a reported in Table 2. As we shall see, this means that, if UC. We may think that the persistence of such condition PERSON+R and AGENT~R, the latter cannot subsume the across time could be a good candidate for a necessary IC former. for φ, since it satisfies (3). However, it fails to satisfy (4), and does not qualify as a necessary identity condition: thus, Identity constraints a UC is a persistence condition, but not an identity condition. φ+I can’t subsume ψ-I (9) As with rigidity, in some situations it maybe important to distinguish properties that do not carry a common UC for Properties with incompatible ICs are disjoint. (10) all its instances, from properties all of whose instances are The first constraint follows immediately from our defini- not intrinsic wholes. As we shall see, an example of the tions, while the second one deserves some comment. An former kind may be Legal Agent, all of whose instances are important point is the difference between different and intrinsic wholes (some people, some companies), however incompatible ICs, related to the fact that they can be inher- there is not a single relation ω for all of them (since persons ited and specialized along taxonomies. Consider the and companies may have different UCs). Amount of Matter domain of abstract geometrical figures, for example, where is usually an example of the latter kind, since none of its the property POLYGON subsumes TRIANGLE. A necessary instances can be intrinsic wholes. Therefore we define: and sufficient IC for polygons is, “Having the same edges Definition 12 A property has anti-unity (~U) if every and the same angles”. On the other hand, an additional nec- instance of the property is not an intrinsic whole. essary and sufficient IC for triangles is, “Having two edges and their internal angle in common” (note that this condi- Of course, ~U implies -U. tion is only-necessary for polygons). So the two properties have different ICs (although they have one IC in common), Dependence but their extensions are not disjoint. On the other hand, The final meta-property we employ as a formal ontological consider AMOUNT OF MATTER and PERSON. If we tool is based on the notion of dependence. This is a very admit mereological extensionality for the former but not for general notion, whose various forms and variations are dis- the latter (since persons can replace their parts), they have cussed in detail in (Simons, 1987). We shall introduce here incompatible ICs, so they must be disjoint (in this case, we a specific kind of dependence, which we call external can’t say that a person is an amount of matter). notional dependence (or simply external dependence), based on Simons’ notional dependence. Intuitively, we say Unity constraints φ ψ that a property is externally dependent on a property if, φ+U can't subsume ψ-U (11) for all its instances x, necessarily some instance of ψ must exist, which is not a part nor a constituent of x. For exam- φ~U can't subsume ψ+U (12) ple, PARENT is externally dependent on CHILD (one can not be a parent without having a child), but PERSON is not Properties with incompatible UCs are disjoint. (13) externally dependent on heart nor on body (because any person has a heart as a part and is constituted of a body). Again, constraints (11-12) trivially follow from our defi- A formal account of this definition requires a definition nitions. As an example of (12), suppose we wonder if VASE of the constitution relationship, which in turn is based on is subsumed by AMOUNT OF CLAY. We may think of a non-extensional mereology (see again Simons’ book). It vase as an amount of clay that has “just” the property of will suffice here to say that x constitutes y if x and y share being a whole, satisfying a suitable UC for vases. In this the same basic parts, and y is existentially dependent on x, case however it would not be an intrinsic whole, since it that is, x cannot actually exist without y actually existing. would remain the same amount of clay after the vase is crashed. This analysis of UCs brings to light a very com- the terms. mon misuse of the subsumption relation, the fact is that vases are constituted of amounts of clay, not subsumed by Entity -I-U-D+R them. Location Amount of matter +O-U-D+R +O~U-D+R Red Agent Group +O+U-D+R Dependence constraints -I-U-D-R -I-U+D~R Physical object Living being φ+D ψ-D can't subsume (14) +O+U-D+R +O+U-D+R Group of people +I-O+U-D+R This constraint trivially follows from our definitions. Social entity Fruit Food +O+U+D+R +O+U-D+R +I-O~U+D~R Animal Legal agent Assumptions +O+U-D+R +O-U+D~R Finally, we make the following assumptions regarding Apple identity, adapted from (Lowe, 1989): +O+U-D+R Vertebrate Organization • Sortal Individuation. Every domain element must instan- +I-O+U-D+R +O+U+D+R tiate some property carrying an IC (+I). In this way we Caterpillar Country Red apple +O+U-D~R satisfy Quine’s dictum “No entity without identity” +O+U+D~R +I-O+U-D~R Butterfly Person (1969). +O+U-D~R +O+U-D+R • Sortal Expandability. If two entities (instances of differ- Figure 1: A messy taxonomy. ent properties) are the same, they must be instances of a property carrying a condition for their identity. In the next steps, the consistency of these assumptions will be validated on the basis of our meta-properties and their constraints. We give here a necessarily brief account of The backbone taxonomy these assumptions, recalling that the point here is not to One of the principal roles of taxonomies is to impart struc- claim that they are correct (though we believe them to be ture on an ontology, to facilitate human understanding, and reasonable), but to explore the consequences of making to enable integration. We have found that a natural result of these assumptions within a particular ontology. our analysis is the identification of special properties Locations can be spatial or temporal regions. Since they (nodes) in a taxonomy that best fill this role. These proper- can be either connected or not, we don’t assume a unity ties form what we call the backbone taxonomy. condition for them. For amounts of matter, we assume that The backbone taxonomy consists only of rigid proper- none of them has a unity condition, thus ~U. Agent is ties. We divide these backbone properties into three kinds: assumed to be anti-rigid to capture the intuition that some- categories, which do not carry identity (-I), types which thing is an agent only while it is involved in an action (we supply identity (+O), and quasi-types which carry but do are therefore not thinking of potential agents). Physical not supply identity (-O+I). A complete analysis of the objects are taken to be isolated material entities (so an property kinds that result from our meta-properties is given apple is a physical object, but an undetached part of it is in (Guarino & Welty, 2000a). not). Vertebrates are thought of as vertebrate animals, not Categories can not be subsumed by any other kinds of just as arbitrary things having a spine. Social entities are properties, and therefore represent the highest level (most thought of as pluralities of living beings exhibiting some general) properties in a taxonomy. They are usually taken kind of “social unity”. Legal agents are conceived as being as primitive properties because defining them is too diffi- involved in a legal contract. Finally, countries are (quite cult (e.g. entity or thing). naively) conceived as geographic regions that have a (not Types are critical in our analysis because according to necessarily permanent) political status. We now continue the assumptions presented above every instance (element of with the next step of our methodology: the domain) instantiates at least one of these properties. 2. C heck the consistency of each set of meta-properties. We Therefore considering only the elements of the backbone have seen that our meta-properties are not independent, gives someone a survey of the entire universe of possible instances. Entity -I-U-D+R

Location Amount of matter A Taxonomy Cleaning Example +O-U-D+R +O~U-D+R Red Agent Group +O+U-D+R -I-U-D-R -I-U+D~R We present now an example of how these meta-properties Physical object Living being Group of people can be used to make modeling assumptions clear, and to +O+U-D+R +O+U-D+R +I-O+U-D+R produce well-founded taxonomies. Figure 1 shows a messy taxonomy, which has mostly Social entity Fruit Food +O+U-D+R been drawn from examples of overloaded is-a relationships +O+U-D+R +I-O~U+D~R Animal Legal agent in existing ontologies. Our methodology proceeds as fol- +O+U-D+R +O-U+D~R lows: Apple Organization +O+U-D+R 1. Make clear the ontological assumptions about each Vertebrate +O+U-D+R property in the taxonomy to in terms of the relevant +I-O+U-D+R Geographical Caterpillar Country meta-properties. To save space, this step is already region +I-O+U-D~R +O+U-D+R shown in Figure 1. The assignment of meta-properties +O+U-D+R Red apple Butterfly Person was made based on deliberately naive – but believable – +I-O+U-D~R +I-O+U-D~R +O+U-D+R assumptions regarding the most common meanings of Figure 2: The COUNTRY case ﬁxed. Entity -I-U-D+R Entity -I-U-D+R

Location Amount of matter Amount of matter Group Physical object Red +O-U-D+R +O~U-D+R +O~U-D+R +O+U-D+R +O-U-D+R -I-U-D-R Agent Social entity Food -I-U+D~R Physical object Living being Group of people +I-O~U+D~R Living being +O+U-D+R +O+U-D+R +O+U-D+R +I-O-U-D+R +O+U-D+R Group +O-U-D+R Social entity Location Legal agent Fruit +O+U+D+R +O-D+R Fruit Animal +O-U-D+R +O-U+D~R +O+U-D+R +O+U-D+R Animal Group of people +O+U-D+R Country +I-O-U-D+R +O+D+R Apple Geographical Vertebrate Organization Apple +O+U-D+R +O+U+D+R region +I-O+U-D+R +O-D+R Vertebrate Organization +O-D+R Country -O+I-D+R +O+D+R Geographical +O+U-D+R Region Person Person Butterfly Caterpillar Red apple +O+U-D+R +O+U-D+R +O-D+R +I-O+U-D~R +I-O+U-D~R +I-O-D~R Figure 4: Restricting to rigid properties. Figure 5: Adding other properties – backbone highlighted. since “own identity” (+O) is only defined for rigid (+R) 5. Add other properties, checking for possible constraint properties. In our case, it seemed natural to assume for violations. In this case, we find that AGENT and LEGAL- COUNTRY both +O and ~R, but this is inconsistent with AGENT are not allowed to subsume PERSON, ORGANI- Definition 7. The inconsistency forces a closer inspection ZATION, and COUNTRY, since ~R can not subsume +R. which reveals that two senses of country (political region It may appear that this results in lost information: previ- and geographical region) have been merged into one, ously we had that a PERSON is a LEGAL-AGENT, where while their identity conditions are pretty different. This did this go? The answer is that, although PERSON is a property is therefore split into two rigid properties, GEO- valid kind of LEGAL-AGENT, it is not the case that all GRAPHICAL REGION and COUNTRY, carrying their persons are legal agents. The is-a relation is not the own identity and unity. COUNTRY is classified under proper way to represent this, a partition of the LEGAL- SOCIAL ENTITY and LEGAL ENTITY (Figure 2). AGENT property, or a specific relation would be more 3. Remove all properties except for the rigid ones. The appropriate. The same analysis holds for FOOD. The result of this process, shown in Figure 3, is the first step result of this step is shown in Figure 5. towards identifying the backbone taxonomy. 4. Check the constraints imposed on each taxonomic rela- 6. Check for missing concepts. We have seen that identity tionship as a consequence of the meta-properties incompatibilities imply disjoint sortals. The reverse may assigned to its arguments. The two links connecting be not necessarily true; for instance, in our case, we PHYSICAL OBJECT and LIVING BEING to AMOUNT know that BUTTERFLY and CATERPILLAR are disjoint OF MATTER have been deleted because they violate the from PERSON although no identity incompatibility unity constraints. The link between ANIMAL and PHYSI- accounts for that. Moreover, we know that caterpillar and CAL OBJECT is removed because of incompatible ICs: butterfly are not disjoint, since the same insect (a lepi- when an animal dies it ceases to exist, however the phys- dopteran) can be a caterpillar at an earlier stage and a ical body remains. ORGANIZATIONs, similarly, are butterfly at a later stage. We have therefore good reasons more than just a group of people, since the same group of to add a new concept, LEPIDOPTERAN, which sub- people can make different organizations. The result of sumes both of them. It supplies its own IC, which will be these operations gives the preliminary backbone taxon- different from those of persons. A more detailed account omy reported in Figure 3. of the lepidopteran case is given in (Guarino and Welty, 2000a).

Entity -I-D+R Entity -I-U-D+R

Amount of matter Amount of matter Physical object Physical object Red +O~U-D+R +O~U-D+R +O+U-D+R +O+U-D+R -I-U-D-R Agent Social entity Food -I-U+D~R Living being Group Social entity +I-O~U+D~R Living being +O+U-D+R +O+U-D+R Location +O-U-D+R +O+U-D+R +O+U-D+R Group +O-U-D+R +O-U-D+R Location Legal agent Fruit +O-D+R Animal Fruit +O-U-D+R +O-U+D~R +O+U-D+R Group of people +O+U-D+R Animal Group of people +I-O-U-D+R +O+U-D+R Country +I-O-U-D+R Vertebrate Geographical +O+D+R Apple +I -O+U-D+R region Lepidopteran Apple +O+U-D+R Vertebrate Organization +O-D+R +O-D+R +O+U-D+R -O+I-D+R +O+D+R Geographical Person Country Organization Region +O+U-D+R +O+U-D+R +O+U-D+R Person Butterfly Caterpillar Red apple +O+U-D+R +O-D+R +I-O+U-D~R +I-O+U-D~R +I-O-D~R Figure 3: The preliminary backbone taxonomy Figure 6: The final taxonomy with highlighted backbone. The final cleaned taxonomy is shown in Figure 6. Note that References one result of this “cleaning” process is the removal of many occurrences of multiple inheritance. This is not necessarily Guarino, N., Carrara, M., and Giaretta, P. 1994. An Ontol- a specific goal, however it naturally follows from the fact ogy of Meta-Level Categories. Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth that, as discussed in (Guarino, 1999), multiple inheritance International Conference (KR94). Morgan Kaufmann. is often used as a tool to represent more than simply sub- Guarino, N. 1998. Some Ontological Principles for Design- sumption – as we found in this example. We believe that ing Upper Level Lexical Resources. Proceedings of LREC- these cases make taxonomies confusing; if the purpose of 98. an ontology is to make the meaning clear, then the meaning Guarino, N. 1999. The Role of Identity Conditions in should not be clouded by using the same mechanism to sig- Ontology Design. In Proceedings of IJCAI-99 workshop on nify more than one thing, since there is no way to disam- Ontologies and Problem-Solving Methods: Lessons biguate the usage. Furthermore, there is at least some Learned and Future Trends. Stockholm, Sweden, IJCAI, empirical evidence derived from studies of programmers Inc.: 2-1 2-7. who maintain object-oriented programs that multiple inher- Guarino, N., and Welty, C. 2000a. A Formal Ontology of itance is confusing and makes taxonomies difficult to Properties. LADSEB/CNR Technical Report 01/2000. understand (Huitt and Wilde, 1992). Available from http://www.ladseb.pd.cnr.it/infor/ontology/ Papers/OntologyPapers.html Guarino, N., and Welty, C. 2000b. Identity, Unity, and Indi- Conclusions viduality: Towards a Formal Toolkit for Ontological Analy- sis. To appear, Proceedings of ECAI-2000. Available from We have presented here the basic steps of a methodology http://www.ladseb.pd.cnr.it/infor/ontology/Papers/Ontolo- for ontology design founded on a formal ontology of prop- gyPapers.html. erties built on a core set of meta properties, which exploits Hirst, G. 1991. Existence Assumptions in Knowledge Rep- the basic notions of identity, rigidity, and dependence. We resentation. Artificial Intelligence, 49: 199-242. have seen how a rigorous analysis based on these notions Huitt, R., and Wilde, N. 1992. Maintenance Support for offers two main advantages to the knowledge engineer: Object-Oriented Programs. IEEE Transactions on Software Engineering. 18(12). • It results in a cleaner taxonomy, due to the semantic con- Lewis, D. 1983. New Work for a Theory of Universals. straints imposed on the is-a relation; Australasian Journal of Philosophy, 61(4). • The backbone taxonomy is identified. Lowe, E. J. 1989. Kinds of Being. A Study of Individuation, Identity and the Logic of Sortal Terms. Basil Blackwell, • It forces the analyst to make ontological commitments Oxford. explicit, clarifying the intended meaning of the concepts Quine, W. V. O. 1969. Ontological Relativity and Other used and producing therefore a more reusable ontology. Essays. Columbia University Press, New York, London. Simons, P. 1987. Parts: a Study in Ontology. Clarendon Press, Oxford. Acknowledgments Strawson, P. F. 1959. Individuals. An Essay in Descriptive Metaphysics. Routledge, London and New York. We are indebted to Bill Andersen, Massimiliano Carrara, Wieringa, R., De Jonge, W., and Spruit, P. 1994. Roles and Pierdaniele Giaretta, Dario Maguolo, Claudio Masolo, dynamic subclasses: a modal logic approach. In Proceed- Chris Partridge, and Mike Uschold for their useful com- ings of European Conference on Object-Oriented Program- ments on earlier versions of this paper. ming. Bologna.